Simple Harmonic Motion and hung spring

In summary, a 0.450-kg block attached to a spring drops 0.150 m before coming to rest. The spring constant can be found by using the equation Ei = Ef, and the angular frequency can be calculated using \omega = sqrt (k/m). During the motion of the spring, two forces act on the block: gravity and the restoring force of the spring. At rest, the sum of the forces is equal to ma, and gravity is pulling harder than the restoring force. However, the block remains at rest due to a careless mistake in calculation.
  • #1
grandprix
28
0

Homework Statement


A spring is hung from the ceiling. A 0.450-kg block is then attached to the free end of the spring. When released from rest, the block drops 0.150 m before momentarily coming to rest. (a) What is the spring constant of the spring? (b) Find the angular frequency of the block’s vibrations.


Homework Equations


Ei = Ef

[tex]\omega[/tex] = sqrt (k/m)


The Attempt at a Solution



I can't figure out how to find part A. I know that once I find that I take that value and plug it into equation 2 to solve for the angular frequency.
 
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  • #2
During the entire motion of the spring two forces act on the block, which two forces?. During the instant the block is at rest how are these two forces related to each other?
 
  • #3
gravity on the block and tension on the spring?
 
  • #4
Technically gravity and the restoring force of the spring. What about my second question?
 
  • #5
sum of the forces = -kx

right?
 
  • #6
No, the sum of the forces=ma. During the instant the block is at rest, which force pulls harder, gravity or the restoring force?
 
  • #7
gravity
 
  • #8
If gravity was pulling harder then why is the block at rest? If it was pulling harder it should be moving down. So same question again!
 
Last edited:
  • #9
Oh jeez i was making a careless mistake, I got the answer now!
 

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion where an object oscillates back and forth around a central equilibrium point, with a restoring force that is directly proportional to the displacement from that point. Examples of simple harmonic motion include a pendulum swinging or a mass attached to a spring bouncing up and down.

2. How does a hung spring exhibit simple harmonic motion?

A hung spring exhibits simple harmonic motion because when it is stretched or compressed from its equilibrium position, it experiences a restoring force that is proportional to its displacement. This results in the spring oscillating back and forth around its equilibrium point, with a period of motion that depends on the mass of the object attached to the spring and the spring's stiffness.

3. What factors affect the period of a hung spring's simple harmonic motion?

The period of a hung spring's simple harmonic motion is affected by the mass of the object attached to the spring, the stiffness of the spring, and the force of gravity. A heavier object will result in a longer period, while a stiffer spring and a higher gravitational force will result in a shorter period.

4. Can the amplitude of simple harmonic motion be changed for a hung spring?

Yes, the amplitude of simple harmonic motion for a hung spring can be changed by adjusting the initial displacement of the object attached to the spring. The farther the object is initially pulled or pushed from the equilibrium point, the greater the amplitude of the motion will be.

5. How is simple harmonic motion related to energy conservation?

Simple harmonic motion is related to energy conservation because, in the absence of external forces, the total mechanical energy of the system (kinetic energy + potential energy) remains constant throughout the motion. As the object oscillates between its maximum displacement from the equilibrium point, the potential energy is converted into kinetic energy, and vice versa, resulting in a continuous exchange of energy. This means that the total energy of the system will always be conserved.

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